Heegaard Floer Homologies: lecture notes

TL;DR

This paper provides lecture notes on Heegaard Floer homology, emphasizing sutured Floer homology, aimed at explaining the concepts and developments in this area of geometric topology.

Contribution

It offers an accessible introduction and overview of Heegaard Floer homology with a focus on sutured Floer homology, consolidating key ideas from a series of lectures.

Findings

Clarifies the relationship between Heegaard Floer and sutured Floer homology

Provides foundational knowledge for further research in 3-manifold topology

Summarizes recent developments in the field

Abstract

These are lecture notes from a series of lectures at the SMF summer school on "Geometric and Quantum Topology in Dimension 3", June 2014. The focus is on Heegaard Floer homology from the perspective of sutured Floer homology.